sage: H = DirichletGroup(5850)
pari: g = idealstar(,5850,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 1440 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{12}\times C_{60}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{5850}(3251,\cdot)$, $\chi_{5850}(3277,\cdot)$, $\chi_{5850}(2251,\cdot)$ |
First 32 of 1440 characters
Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.
Character | Orbit | Order | Primitive | \(-1\) | \(1\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{5850}(1,\cdot)\) | 5850.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{5850}(7,\cdot)\) | 5850.ed | 12 | no | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(i\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(i\) | \(i\) |
\(\chi_{5850}(11,\cdot)\) | 5850.gz | 60 | no | \(1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{5850}(17,\cdot)\) | 5850.hg | 60 | no | \(1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{1}{12}\right)\) |
\(\chi_{5850}(19,\cdot)\) | 5850.gy | 60 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{5850}(23,\cdot)\) | 5850.hf | 60 | no | \(1\) | \(1\) | \(i\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(i\) |
\(\chi_{5850}(29,\cdot)\) | 5850.fs | 30 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{5850}(31,\cdot)\) | 5850.hb | 60 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{5850}(37,\cdot)\) | 5850.ga | 60 | no | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{11}{12}\right)\) |
\(\chi_{5850}(41,\cdot)\) | 5850.gu | 60 | no | \(1\) | \(1\) | \(i\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(-1\) |
\(\chi_{5850}(43,\cdot)\) | 5850.dq | 12 | no | \(-1\) | \(1\) | \(i\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(i\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(-1\) | \(i\) |
\(\chi_{5850}(47,\cdot)\) | 5850.gb | 60 | no | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{11}{12}\right)\) |
\(\chi_{5850}(49,\cdot)\) | 5850.ca | 6 | no | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(-1\) |
\(\chi_{5850}(53,\cdot)\) | 5850.er | 20 | no | \(1\) | \(1\) | \(-i\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(i\) |
\(\chi_{5850}(59,\cdot)\) | 5850.gr | 60 | no | \(1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{5850}(61,\cdot)\) | 5850.eh | 15 | no | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(1\) |
\(\chi_{5850}(67,\cdot)\) | 5850.fw | 60 | no | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(i\) |
\(\chi_{5850}(71,\cdot)\) | 5850.gx | 60 | no | \(1\) | \(1\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{5850}(73,\cdot)\) | 5850.ej | 20 | no | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(-i\) |
\(\chi_{5850}(77,\cdot)\) | 5850.hc | 60 | no | \(1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{1}{12}\right)\) |
\(\chi_{5850}(79,\cdot)\) | 5850.fp | 30 | no | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{5850}(83,\cdot)\) | 5850.gb | 60 | no | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{5}{12}\right)\) |
\(\chi_{5850}(89,\cdot)\) | 5850.gp | 60 | no | \(1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{5850}(97,\cdot)\) | 5850.fw | 60 | no | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(i\) |
\(\chi_{5850}(101,\cdot)\) | 5850.bx | 6 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{5850}(103,\cdot)\) | 5850.gg | 60 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{7}{12}\right)\) |
\(\chi_{5850}(107,\cdot)\) | 5850.ds | 12 | no | \(1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{12}\right)\) |
\(\chi_{5850}(109,\cdot)\) | 5850.em | 20 | no | \(-1\) | \(1\) | \(-i\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(1\) |
\(\chi_{5850}(113,\cdot)\) | 5850.hi | 60 | no | \(1\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{11}{12}\right)\) |
\(\chi_{5850}(119,\cdot)\) | 5850.gr | 60 | no | \(1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{5850}(121,\cdot)\) | 5850.fr | 30 | no | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{5850}(127,\cdot)\) | 5850.gk | 60 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{5}{12}\right)\) |